The present invention relates to a safety device for power supply systems utilizing synchronous machines, and more particularly to a protection circuit for damping the subsynchronous natural resonant frequency signals which can be damaging to a shaft connecting a turbine to a generator in a turbine generator power supply system.
The stability of a synchronous generator can be greatly reduced or possibly even eliminated when the inductive reactance between the generator and a high-voltage power line reaches high levels due to very long transmission lines. In order to overcome this problem, it is a common practice, particularly in the United States, to compensate for the large reactance of the long lines by as much as 60 to 80% through the use of capacitors connected in series with the transmission lines. Such a compensated system is shown in simplified configuration in the schematic circuit diagram of FIG. 1 in which a generator is connected to a network by a single transmission line. The reactances x.sub.G of the generator G, x.sub.T of the block transformer T, -x.sub.C of the series connected compensation capacitor C and x.sub.L of the transmission line L of the power transmission network N are generally greater than the resistances r.sub.G, r.sub.T, and r.sub.L of generator G, block transformer T and network N, respectively, and therefore play a major factor in determining the output current value. By way of example, the numerical values of the reactances for the components illustrated in FIG. 1 can be x.sub.G =0.145, x.sub.T =0.14, x.sub.C =0.371 and x.sub.L =0.53 at a rated line frequency of 60 Hz.
The total inductive reactance .SIGMA..sub.x between the generator G and the power supply network N increases linearly with the frequency .omega. of the current in the system, as illustrated in FIG. 2a by curve 1. The capacitor C connected in series with the transmission line acts as a negative reactance which is inversely proportional to the frequency .omega., i.e. as the frequency increases, the absolute value of the reactance decreases as shown at curve 2 in FIG. 2a. In FIG. 2b, the resulting reactance .SIGMA..sub.x between the internal subtransient voltage of the generator and the power supply system voltage, namely ##EQU1## is plotted as a function of .omega., wherein .omega..sub.n is the rated line frequency of the power supply system, e.g. 60 Hz. The electrical resonant frequency .omega..sub.e of the system is defined as: ##EQU2## and the total reactance of the circuit is zero at this frequency.
During certain dynamic processes, such as load decreases or automatic reclosing of short-circuiting safety devices such as a circuit breaker S or a spark-over device to add additional capacitance (as illustrated in FIG. 1), the capacitive reactance of the supply system will be varied such that resonant currents at the electrical resonance frequency .omega..sub.e will be produced if the initial conditions of the system are proper. In conjunction with the rated frequency .omega..sub.n of the supply system, these currents will generate electrical air-gap torques which pulse at the differential frequency EQU .omega..sub.n -.omega..sub.e.
If this pulsing torque frequency coincides with one of the natural mechanical frequencies .omega..sub.m of the shaft connecting the turbine to the generator, i.e. EQU .omega..sub.m =.omega..sub.n -.omega..sub.e,
an electromechanical resonance will occur. The mechanical torque in the shaft can increase to inadmissibly high values. Furthermore, since a synchronous machine running at a rated speed but generating current having a frequency less than the rated frequency .omega..sub.n acts as an asynchronous generator, it is entirely possible that the electromechanical resonance from the generator will be reinforced by the asynchronous output signal. In such a case, the mechanical torque in the shaft can increase to such a point that the shaft will rupture.
In the past, it has been known to protect a turbine generator from subsynchronous resonance by means of a filter such as that shown in FIG. 3a, in which those currents having frequencies which cause a subsynchronous resonance in the shaft are screened out. This screening filter is usually short-circuited during normal operation of the supply system, and is connected in series with the power supply circuit by means of a control member when a subsynchronous resonance is detected. When the filter is switched into the circuit, the response of the resulting circuit reactance to the frequency of the current is modified. The reactance of the circuit when the filter is switched in is illustrated in solid lines in FIG. 3b and contrasted with the reactance existing prior to connection of the filter, which is illustrated by the dashed line. It can be seen that the filter is designed so that the reactance of the network is infinitely great in the vicinity of the mechanical natural frequency .omega..sub.n -.omega..sub.m when the filter is switched into the circuit. It is equal to zero, however, for the frequencies .omega..sub.1 and .omega..sub.2. Thus, only currents at the frequencies .omega..sub.1 and .omega..sub.2 can appear during the dynamic process in which the filter is connected to the power supply circuit. Since no current will flow at the electromechanical resonance frequency .omega..sub.n -.omega..sub.m, no mechanical torque will appear at the mechanical natural frequency .omega..sub.m of the shaft. Accordingly, a subsynchronous resonance is prevented.
Filters of this type can be installed at the neutral point of the generator or the block transformer, for example. Further details of such a system are described in U.S. Pat. No. 3,813,593 and in Volume 37 of Proceedings of the American Power Conference, 1975, at pp. 916-922.
The shaft of a turbine generator can have a number of natural frequencies. For this reason, the filter must be designed for a number of frequencies .omega..sub.m(1), .omega..sub.m(2), . . . . As the number of natural frequencies increases, the cost of the filter and the difficulty of precise adjustment of the filter will be correspondingly increased.
The connection of one or more filters which are synchronized to the natural mechanical frequencies .omega..sub.m of the shaft presents a number of other disadvantages. The natural frequencies .omega..sub.m of the shaft can be determined only within certain tolerances. Therefore, the adjustment of the filter to tune it to these frequencies can be difficult and provide less than satisfactory results. In addition, the response characteristics of the filter are dependent upon temperature and therefore vary under differing conditions.
In many cases, the resistance of the transmission lines is so small that currents at the frequencies .omega..sub.1, .omega..sub.2, (previously defined with respect to FIG. 3b) are not adequately damped. These currents and the electrical exciting torques which accompany them can increase to a large degree in cases in which signals at the frequencies .omega..sub.n -.omega..sub.1 and .omega..sub.n -.omega..sub.2 are present in the supply system. The mechanical torques which are consequently induced in the shaft can likewise achieve high values in spite of the filters.
Furthermore, the short circuiting of the filter to remove it from the circuit after completion of a dynamic event presents an uneven transition in the total system reactance. Under certain circumstances, this transition can cause another transient phenomenon which will require the filter to be connected to the circuit again, making it difficult to achieve a steady-state condition.
Another proposed solution for damping the subsynchronous resonances consists of placing a resistor in shunt with one or more of the compensation capacitors between the block transformer and the network. In the event that energy losses in the shunt resistance become too great, the power frequency current is diverted away from the shunt resistance by means of a relatively simple resonant circuit. Such a solution using a shunt resistor is described in the article appearing in IEEE Transactions PAS-90, Vol. 3, 1971, pp. 1305-1311, and more particularly at page 1309 in the lefthand column. This proposed solution presents undesired interventions in the transmission network and accompanying power losses. Furthermore, it is expensive due to the cost of damping circuits which are rated for the high-voltage of the power supply system.